Question

Give the complete symbol \(\left(^{A}_{Z} X\right),\) including atomic number and mass number, for each of the following atoms: (a) magnesium with 15 neutrons, (b) titanium with 26 neutrons, and (c) zinc with 32 neutrons.

Short answer

(a) \(^{27}_{12} \text{Mg}\), (b) \(^{48}_{22} \text{Ti}\), (c) \(^{62}_{30} \text{Zn}\).

Step-by-step solution

Understand the Components of \\(^{A}_{Z} X\\)

The symbol \(^{A}_{Z} X\) represents an element where \(A\) is the mass number, \(Z\) is the atomic number, and \(X\) is the chemical symbol of the element. Mass number \(A\) is the sum of protons and neutrons.

Compute Mass Number for Magnesium

For magnesium with 15 neutrons, first find its atomic number (\(Z\)). Magnesium (Mg) has an atomic number of 12. Mass number \(A = Z + ext{neutrons} = 12 + 15 = 27\). Thus, magnesium's symbol is \(^{27}_{12} \text{Mg}\).

Compute Mass Number for Titanium

For titanium with 26 neutrons, first find its atomic number (\(Z\)). Titanium (Ti) has an atomic number of 22. Mass number \(A = Z + ext{neutrons} = 22 + 26 = 48\). Thus, titanium's symbol is \(^{48}_{22} \text{Ti}\).

Compute Mass Number for Zinc

For zinc with 32 neutrons, first find its atomic number (\(Z\)). Zinc (Zn) has an atomic number of 30. Mass number \(A = Z + ext{neutrons} = 30 + 32 = 62\). Thus, zinc's symbol is \(^{62}_{30} \text{Zn}\).

Key concepts

Atomic Number

The atomic number is a fundamental property of a chemical element. It is defined as the number of protons found in the nucleus of an atom. This number is denoted as \(Z\). Since protons have a positive charge, the atomic number also determines the electrical charge of the nucleus.

Every element on the periodic table has a unique atomic number that distinguishes it from other elements. For example:

• Hydrogen has an atomic number of 1, which means there is 1 proton in its nucleus.
• Sodium has an atomic number of 11, indicating 11 protons.
• In our exercise, magnesium has an atomic number of 12, titanium 22, and zinc 30.

The atomic number is crucial because it defines the identity of an element. When you know the atomic number, you can determine other properties of the atom, such as its electron configuration and chemical behavior.

Mass Number

The mass number represents the total number of protons and neutrons in an atom's nucleus. It is denoted by \(A\). To calculate the mass number, you simply add the number of protons (the atomic number \(Z\)) to the number of neutrons.

Here’s how it works:

• For magnesium, with 15 neutrons and an atomic number of 12, the mass number is \(A = 12 + 15 = 27\).
• For titanium, with 26 neutrons and an atomic number of 22, \(A = 22 + 26 = 48\).
• For zinc, with 32 neutrons and an atomic number of 30, \(A = 30 + 32 = 62\).

Unlike the atomic number, the mass number is not unique for every element. Elements can have the same chemical identity but different numbers of neutrons, leading to different mass numbers. These are called isotopes. For example, carbon-12 and carbon-14 are isotopes of carbon.

Chemical Elements

Chemical elements are pure substances consisting entirely of one type of atom, defined by their atomic number. Each element is represented by a unique chemical symbol, usually comprising one or two letters. Examples include H for hydrogen, Mg for magnesium, and Zn for zinc.

Elements are organized in the periodic table, which groups them by similar chemical properties. This arrangement helps in predicting how elements will react with each other in chemical reactions.

• Each element's position in the table reflects its electron configuration.
• The periodic table not only classifies elements but also provides important information like atomic number and typical mass.

Understanding chemical elements is essential in the study of chemistry, as it forms the basis for understanding matter and its interactions. This knowledge allows chemists to synthesize new compounds and materials for various applications, from pharmaceuticals to industrial products.